a is a negative number.
b is a positive number.
Therefore, a - b is....?
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a is a negative number.
b is a positive number.
Therefore, a - b is....?
We test using an example:
We define that
a = -1
b = 2
Now we replace in the exercise:
-1-(2) = -1-2 = -3
In this case, the result is negative!
We test a case where the value of b is less than a
We define that
a = -2
b = 1
-2-(1) = -2-1 = -3
In this case, the result is again negative.
Since it is not possible to produce a case where a is greater than b (because a negative number is always less than a positive number),
The result will always be the same: "negative", and that's the solution!
Negative
What will be the sign of the result of the next exercise?
\( (-2)\cdot(-4)= \)
Think of it on a number line! Starting at a negative position and subtracting (moving left) a positive amount takes you further into negative territory. You can never reach zero or positive numbers this way.
Even if b = 0.001, subtracting it from any negative number still gives a negative result! For example: -5 - 0.001 = -5.001. The size doesn't matter - the direction does.
That's addition of two negatives, which also gives negative. But here we have subtraction: a - b = a + (-b). So -2 - 3 becomes -2 + (-3) = -5.
Absolutely! Think of temperature: if it's -5°C and drops by 3 more degrees, you get -8°C. Or money: owing 3 more means you owe $8 total.
Remember the pattern: negative - positive = more negative. You can also rewrite as addition: a - b = a + (-b), then add the absolute values and keep the negative sign.
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